In a polishing step of a glass substrate which is used for manufacturing a hard disk, a photomask or the like and requires high-precision smoothness, a colloidal silica-containing polishing slurry (colloidal silica slurry) has been used. However, the polishing step using the colloidal silica slurry has a slow polishing rate, compared to conventional polishing steps using cerium oxide, and is applied to only finish polishing in many cases. Accordingly, various attempts have been made as methods for increasing the polishing rate (for example, see Patent Documents 1 and 2).